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Tagged with ca.classical-analysis-and-odes harmonic-analysis
54 questions with no upvoted or accepted answers
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Fourier restriction in decoupling inequalities
I'm reading Bourgain and Demeter's paper https://arxiv.org/abs/1403.5335 "The proof of the $l^2$ decoupling conjecture".
On page 1 the paper says, let $P^{n-1}=\{(\xi_1,...,\xi_{n-1},\xi_1^2+...
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Does there exists $f\in A_{\mathbb R}(\mathbb T)$ with $||f||=r$ such that $||e^{if}||=e^{r}$?
Let $\mathbb Z$, the set of integers, be a group with respect to addition and its dual group is the $\mathbb T = \{z\in \mathbb C : |z|=1\}$ , one dimensional torus. Put,
$\ell^{1}(\mathbb Z)= \{g:\...
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High dimensional beta integral (question following the previous post)
Hello,
This post is a question following the previous post. In one dimensional case, we have
$$
\int_0^x |y|^{1-\alpha} |x-y|^{1-\beta} d y = \frac{\Gamma(\alpha)\Gamma(\beta)}{\Gamma(\alpha+\beta)} |...
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Harmonic function in infinite domain in $\mathbb{R}^3$, constant on the boundary and decaying as $1/r^2$
EDIT: Let $\Omega\subset \mathbb{R}^3$ be a bounded domain with smooth connected boundary. Let $f\colon \mathbb{R}^3\backslash \Omega \to \mathbb{R}$ be a continuous function which is harmonic in $\...
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